Question

find the exact area of the surface obtained by rotating the curve about the x-axis. y=sqrt(1+5x) 1 13 years ago

Answer 1

i tend to get these mixed up; length of a curve is ds, surface area is 2pi ds, accounting for y or x depending on axis rotated about right?

Answer 2

circumference of a circle is: 2pi r, and in this case r = y(x)

ds amounts to the length of a line segment: ds = sqrt(x'^2+y'^2)

Answer 3

therefore the surface area is:
\[\int_{1}^{7}2\pi~y(x)~ds\]

\[2\pi\int_{1}^{7}y~\sqrt{1+(y')^2}~dx\]